题解
1001 Azshara's deep sea
Unsolved.
1002 Blow up the city.
题解：倒着建图，然后将原图出度为零的点用一个新节点连接起来，支配树板题。
参考代码：
#include<bits/stdc++.h> using namespace std; #define LL long long #define pb push_back //DAG图q个询问,给你u,v:去掉一个点连同和这个点相连的所有边使得u或v不能到达出度为零的点的方案 const int maxn=2e5+7; int n,m,deg[maxn],rt,a[maxn],dep[maxn],val[maxn]; int f[maxn][20]; vector<int>E[maxn],RE[maxn]; void Topsort() { queue<int>q; rt=n+1;//图可能不连通,建一个新点连接起来 for(int i=1;i<=n;i++) if(!deg[i]){q.push(i);E[rt].pb(i);RE[i].pb(rt);} int tot=0; while(!q.empty()) { int u=q.front(); q.pop(); a[++tot]=u; for(auto &v:E[u]){if((--deg[v])==0) q.push(v);} } } int LCA(int x,int y) { if(dep[x]>dep[y]) swap(x,y); for(int i=19;i>=0;i--) { if(dep[y]>dep[x]&&dep[f[y][i]]>=dep[x]) y=f[y][i]; } if(x==y) return x; for(int i=19;i>=0;i--) { if(f[x][i]!=f[y][i]) x=f[x][i],y=f[y][i]; } return f[x][0]; } void Work() { dep[rt]=1; for(int i=1;i<=n;i++) { int u=a[i],fa=-1; for(auto &v:RE[u]) fa=(fa==-1? v:LCA(fa,v)); dep[u]=dep[fa]+1; f[u][0]=fa; for(int i=1;i<=19;i++) f[u][i]=f[f[u][i-1]][i-1]; } } int main() { int tt; scanf("%d",&tt); while(tt--) { scanf("%d%d",&n,&m); memset(f,0,sizeof(f)); for(int i=1;i<=n+1;i++) { E[i].clear(); RE[i].clear(); dep[i]=deg[i]=0; } while(m--) { int u, v; scanf("%d%d", &u, &v); E[v].pb(u); RE[u].pb(v); deg[u]++; } Topsort(); Work(); int q; scanf("%d", &q); while(q--) { int u, v; scanf("%d%d",&u,&v); int lca=LCA(u,v); printf("%d\n",dep[u]+dep[v]-dep[lca]-1); } } return 0; }
1003 Yukikaze and Demons
Unsolved.
1004 Distribution of books
https://blog.csdn.net/liufengwei1/article/details/97703075
#include<bits/stdc++.h> using namespace std; #define maxl 200010 int n,tot,cnt,k; long long up,dow,ans; int a[maxl],b[maxl],dp[maxl],h[maxl],c[maxl]; long long sum[maxl]; long long num[maxl]; inline void prework() { scanf("%d%d",&n,&k); up=0;dow=0; for(int i=1;i<=n;i++) { scanf("%d",&a[i]); sum[i]=sum[i-1]+a[i],num[i]=sum[i]; if(a[i]>0) up+=a[i]; else dow+=a[i]; } num[n+1]=0; sort(num+1,num+2+n); tot=unique(num+1,num+2+n)-num-1; for(int i=0;i<=n;i++) b[i]=lower_bound(num+1,num+1+tot,sum[i])-num; } inline void upd(int i,int x) { int t; while(i<=tot && i) { h[i]=c[i]; for(int k=1;k<(i&-i);k<<=1) h[i]=max(h[i],h[i-k]); i+=i&-i; } } inline int qry(int l,int r) { int ret=-n-1,len=r-l+1; while(len && r) { if(len<(r&-r)) { ret=max(ret,c[r]); r--;len--; }else { ret=max(ret,h[r]); len-=(r&-r); r-=r&-r; } } return ret; } inline bool jug(long long mid) { for(int i=1;i<=n;i++) dp[i]=0; for(int i=1;i<=tot;i++) h[i]=-n-1,c[i]=-n-1; int l=1,r=n,id,tmp; c[b[0]]=0;upd(b[0],c[b[0]]); for(int i=1;i<=n;i++) { id=lower_bound(num+1,num+1+tot,sum[i]-mid)-num; if(id>tot) continue; tmp=qry(id,tot); if(tmp<=-n-1) continue; dp[i]=max(dp[i],qry(id,tot)+1); c[b[i]]=max(c[b[i]],dp[i]); upd(b[i],c[b[i]]); if(dp[i]>=k) return true; } return false; } inline void mainwork() { long long l=dow,r=up,mid; while(l+1<r) { mid=(l+r)>>1; if(jug(mid)) r=mid; else l=mid; } if(jug(l)) ans=l; else ans=l+1; } inline void print() { printf("%lld\n",ans); } int main() { int t; scanf("%d",&t); for(int i=1;i<=t;i++) { prework(); mainwork(); print(); } return 0; }
1005 Easy Math Problem
Unsolved.
1006 Fansblog
#include<bits/stdc++.h> using namespace std; typedef long long LL; unordered_map<LL,LL> mp; LL quick_pow(LL a,LL b,LL mod) { LL ans=1; while(b) { if(b&1) ans=((__int128)ans)*a%mod; a=((__int128)a)*a%mod; b>>=1; } return ans; } long long factor[110], cnt; long long Mul_Mod(long long a, long long b, long long c) { if (b == 0) return 0; long long ans = Mul_Mod(a, b / 2, c); ans = (ans * 2) % c; if (b % 2) ans = (ans + a) % c; return ans; } long long Pow_Mod(long long a, long long b, long long c) { if (b == 0) return 1; long long x = Pow_Mod(a, b / 2, c); if (x == 0) return 0; long long y = Mul_Mod(x, x, c); if (y == 1 && x != 1 && x != c - 1) return 0; if (b % 2) y = Mul_Mod(y, a, c); return y; } bool Miller_rabin(long long n, int timenum = 10) { if (n < 2) return false; if (n == 2) return true; while (timenum--) { if (Pow_Mod(rand() % (n - 2) + 2, n - 1, n) != 1) return false; } return true; } long long Gcd(long long a, long long b) { long long t; while (b) { t = a; a = b; b = t % b; } return a; } void Pollard(long long n); void Factor(long long n) { long long d = 2; while (true) { if (n % d == 0) { Pollard(d); Pollard(n / d); return; } d++; } } void Pollard(long long n) { if (n == 1) return; if (Miller_rabin(n)) { factor[cnt++] = n; return; } long long i = 0, k = 2, x, y, d; x = y = rand() % (n - 1) + 1; while (i++ < 123456) { x = (Mul_Mod(x, x, n) + n - 1) % n; d = Gcd((y - x + n) % n, n); if (d != 1) { Pollard(d); Pollard(n / d); return; } if (i == k) { y = x; k *= 2; } } Factor(n); } int main() { int t; scanf("%d",&t); LL p; while(t--) { scanf("%lld",&p); if(mp.count(p)) { printf("%lld\n",mp[p]); continue; } LL ans=p-1; if(Miller_rabin(p-2)) { LL ret=(LL)(((__int128)(p-1))*quick_pow(p-1,p-2,p)%p); mp[p]=ret; printf("%lld\n",ret); continue; } for(LL i=p-4;i>=998244353;i-=2) { ans=(__int128)ans*(i+1)%p*(i+2)%p; if(Miller_rabin(i)) { LL ret=(LL)(((__int128)(p-1))*quick_pow(ans,p-2,p)%p); mp[p]=ret; printf("%lld\n",ret); break; } } } }
1007 Find the answer
#include<bits/stdc++.h> #define maxl 200010 using namespace std; int n,m; int a[maxl],dy[maxl],ans[maxl]; struct anode { int id,val; }aa[maxl]; struct node { int l,r; long long sum; }tree[maxl*4]; int b[maxl]; inline bool cmp(const anode &x,const anode &y) { return x.val<y.val; } inline void add(int i,int x) { while(i<=n) { b[i]+=x; i+=i&-i; } } inline int sum(int i) { int ret=0; while(i) { ret+=b[i]; i-=i&-i; } return ret; } inline void build(int k,int l,int r) { tree[k].l=l;tree[k].r=r; if(l==r) { tree[k].sum=aa[l].val; return; } int mid=(l+r)>>1; build(k<<1,l,mid); build(k<<1|1,mid+1,r); tree[k].sum=tree[k<<1].sum+tree[k<<1|1].sum; } inline void prework() { scanf("%d%d",&n,&m); for(int i=1;i<=n;i++) scanf("%d",&a[i]),aa[i].id=i,aa[i].val=a[i]; sort(aa+1,aa+1+n,cmp); for(int i=1;i<=n;i++) { dy[aa[i].id]=i; b[i]=0; } for(int i=1;i<=n;i++) add(i,1); build(1,1,n); } inline void upd(int k,int l) { if(tree[k].l==tree[k].r) { tree[k].sum=0; return; } int mid=(tree[k].l+tree[k].r)>>1; if(l<=mid) upd(k<<1,l); else upd(k<<1|1,l); tree[k].sum=tree[k<<1].sum+tree[k<<1|1].sum; } inline int query(int k,long long res) { if(tree[k].l==tree[k].r) { if(tree[k].sum>res) return tree[k].l-1; else return tree[k].l; } if(tree[k<<1].sum<res) return query(k<<1|1,res-tree[k<<1].sum); else return query(k<<1,res); } inline void mainwork() { int l; for(int i=n;i>=1;i--) { upd(1,dy[i]); add(dy[i],-1); l=query(1,m-a[i]); ans[i]=(i-1)-sum(l); } } inline void print() { for(int i=1;i<=n;i++) printf("%d ",ans[i]); puts(""); } int main() { int t; scanf("%d",&t); for(int i=1;i<=t;i++) { prework(); mainwork(); print(); } return 0; }
1008 Game
Unsolved.
1009 K Subsequence
https://blog.csdn.net/baiyifeifei/article/details/97706037
#include<bits/stdc++.h> using namespace std; typedef pair<int, int> pii; const int maxn = 1e4; const int inf = 0x3f3f3f3f; struct edge { int to, cap, cost, rev; edge() {} edge(int to, int _cap, int _cost, int _rev) :to(to), cap(_cap), cost(_cost), rev(_rev) {} }; int V, H[maxn + 5], dis[maxn + 5], PreV[maxn + 5], PreE[maxn + 5]; vector<edge> G[maxn + 5]; void init(int n) { V = n; for (int i = 0; i <= V; ++i)G[i].clear(); } void AddEdge(int from, int to, int cap, int cost) { G[from].push_back(edge(to, cap, cost, G[to].size())); G[to].push_back(edge(from, 0, -cost, G[from].size() - 1)); } int Min_cost_max_flow(int s, int t, int f, int& flow) { int res = 0; fill(H, H + 1 + V, 0); while (f) { priority_queue <pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>> > q; fill(dis, dis + 1 + V, inf); dis[s] = 0; q.push(pair<int, int>(0, s)); while (!q.empty()) { pair<int, int> now = q.top(); q.pop(); int v = now.second; if (dis[v] < now.first)continue; for (int i = 0; i < G[v].size(); ++i) { edge& e = G[v][i]; if (e.cap > 0 && dis[e.to] > dis[v] + e.cost + H[v] - H[e.to]) { dis[e.to] = dis[v] + e.cost + H[v] - H[e.to]; PreV[e.to] = v; PreE[e.to] = i; q.push(pair<int, int>(dis[e.to], e.to)); } } } if (dis[t] == inf)break; for (int i = 0; i <= V; ++i)H[i] += dis[i]; int d = f; for (int v = t; v != s; v = PreV[v])d = min(d, G[PreV[v]][PreE[v]].cap); f -= d; flow += d; res += d*H[t]; for (int v = t; v != s; v = PreV[v]) { edge& e = G[PreV[v]][PreE[v]]; e.cap -= d; G[v][e.rev].cap += d; } } return res; } int a[maxn]; int main() { int t; scanf("%d",&t); while(t--) { int n,k; scanf("%d%d",&n,&k); for(register int i=1;i<=n;++i) scanf("%d",&a[i]); int ss=0,s=1,t=2*n+2,tt=2*n+3; init(tt+1); AddEdge(ss,s,k,0); AddEdge(t,tt,k,0); for(register int i=1;i<=n;++i) { AddEdge(s,i+1,1,0); AddEdge(i+1+n,t,1,0); AddEdge(i+1,i+1+n,1,-a[i]); for(register int j=i+1;j<=n;++j) { if(a[j]>=a[i]) { AddEdge(1+i+n,1+j,1,0); } } } int ans=0; printf("%d\n",-Min_cost_max_flow(ss,tt,inf,ans)); } return 0; }
1010 Sindar's Art Exhibition
Unsolved.
1011 Squrirrel
Unsolved.